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The Research Of Sparse Non-negative Matrix Factorization

Posted on:2020-11-19Degree:MasterType:Thesis
Country:ChinaCandidate:Y F HuFull Text:PDF
GTID:2370330596995000Subject:Control Science and Engineering
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Matrix decomposition refers to the reduction of dimension by decomposing a high-dimensional matrix into several low-dimensional matrices.This technology is widely used in fields such as signal processing,computer vision,audio and video,and image processing.This method can find low-dimensional representations of high-dimensional data,revealing hidden connections behind seemingly unrelated data.The traditional matrix decomposition method mainly decomposes the original high-dimensional matrix V into the product form of two low-dimensional matrices W and H by adding different constraints.But may contain negative elements in two low-dimensional matrices.Due to the existence of these negative elements,there is no direct physical meaning in some practical life scenarios,such as face detection,video tracking,etc.Based on this,the non-negative matrix decomposition algorithm(NMF)came into being and quickly attracted the attention of many scholars at home and abroad.The addition of non-negative constraints makes the decomposition algorithm have a physical meaning that is easy to understand intuitively.A useful property of NMF is that its solution is usually sparse,which makes its local features more obvious.Sparseness is an important feature in many application scenarios.However,the sparsity feature is not the goal of designing the NMF algorithm at first,but a by-product,so the quality of sparsity cannot be guaranteed.In order to make the sparseness of the solution meet the requirements of practical applications,the corresponding sparsity constraint must be added on the basis of the objective function of the traditional NMF algorithm.In this paper,the basic techniques of the sparse non-negative matrix factorization algorithm are studied and studied,mainly based on the N2 algorithm of L2 norm constraint,including the design of the objective function and the derivation of the iterative formula and the verification of the convergence of the algorithm.The specific arrangement of the thesis is as follows: Firstly,the research progress and current situation of NMF,especially sparse NMF at home and abroad are introduced,and the basic theory of NMF is simply summarized and summarized.Then a constrained non-negative matrix factor of fixed L2 norm is designed.Algorithm;finally,the convergence of the proposed algorithm and the constraints of the proposed fixed L2 norm are verified in the experimental part.The specific content of this article is as follows:A constrained NMF algorithm with fixed L2 norm is proposed,which guarantees that the L2 norm of the solution is fixed during the iterative process.Firstly,the Lagrange multiplier method is used to transform the original constrained optimization problem into an unconstrained optimization problem.Then the modified gradient descent method is used to solve the update formula so that the formula can always satisfy the L2 norm fixed in the iterative process.The formula can automatically select the appropriate Lagrangian multiplier and learning rate during the iteration process to ensure that the proposed algorithm satisfies all constraints.The experimental results show that the algorithm is convergent and satisfies the L2 fixed constraint.
Keywords/Search Tags:Non-negative matrix factorization, Sparsity, L2-norm, Lagrange multiplier, Gradient descent algorithm
PDF Full Text Request
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